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   "source": [
    "# PyTorch – 深度学习全栈工程师进阶案例实战（第十期）第5课书面作业\n",
    "学号：115539\n",
    "\n",
    "**作业内容：**  \n",
    "1. Transfer Learning, Multi-task Learning, AutoML和我们的Meta Learning的不同与形同\n",
    "2. 给出cos(mx), cos(m + x), cos(x) - m的泰勒展开"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 第1题\n",
    "Transfer Learning, Multi-task Learning, AutoML和我们的Meta Learning的不同与形同"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**答：**  \n",
    "1. **Transfer Learning**，即迁移学习，其学习的过程中，模型已经确定，并有部分参数继承了预训练模型的参数，然后学习的目的与输出是，学到最优化的权值。  \n",
    "2. **Multi-task Learning**，即多任务学习，其模型也是handcrafted的，只是这个模型同时适用于多种任务，学习的输出也是模型的优化权值。  \n",
    "3. **AutoML**，可以映射为meta learning, 即可以用一个网络模型去预测另一个网络模型。\n",
    "4. **Meta learning**, 是学习如何学习，其输入是多种任务（不同任务中有训练、测试集与模型），其学习的输出是网络模型，说白了就是用一个网络模型去预测另一个网络模型。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 第2题\n",
    "给出cos(mx), cos(m + x), cos(x) - m的泰勒展开\n",
    "\n",
    "**答：**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\cos(mx)=\\sum_{k=0}^{\\infty}\\frac{(-1)^k}{(2k)!}m^{2k}x^{2k}=1-\\frac{1}{2!}m^2x^2+\\frac{1}{4!}m^4x^4-\\frac{1}{6!}m^6x^6+... \n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\cos(m+x)=\\sum_{k=0}^{\\infty}\\frac{(-1)^k}{(2k)!}(x+m)^{2k}=1-\\frac{1}{2!}(m+x)^2+\\frac{1}{4!}(m+x)^4-\\frac{1}{6!}(m+x)^6+... \n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\cos(x)-m=-m+\\sum_{k=0}^{\\infty}\\frac{(-1)^k}{(2k)!}(x)^{2k}=1-m+\\frac{1}{2!}x^2+\\frac{1}{4!}x^4-\\frac{1}{6!}x^6+... \n",
    "$$"
   ]
  }
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